Solve for $x$ : $x^2 - x - 72 = 0$
Answer: The coefficient on the $x$ term is $-1$ and the constant term is $-72$ , so we need to find two numbers that add up to $-1$ and multiply to $-72$ The two numbers $8$ and $-9$ satisfy both conditions: $ {8} + {-9} = {-1} $ $ {8} \times {-9} = {-72} $ $(x + {8}) (x {-9}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 8) (x -9) = 0$ $x + 8 = 0$ or $x - 9 = 0$ Thus, $x = -8$ and $x = 9$ are the solutions.